Probabilidad Matematica

1. Sea el experimento que consiste en sacar una bola de una bolsa en la que se encuentran 10 bolas numeradas de 1 al 10, escribir el espacio muestral. Siendo el suceso A1,2,4,5,8, sea el suceso B5,6,8,9,10y el suceso C 1,3,5,7,9. Calcular AB, BC, AC, C B.
Demostrar las propiedades distributiva, de simplificación entre B y C y las leyes de Morgan con los sucesos A y C.
AB= 1,2,4,5,85,6,8,9,10 ={1,2,4,5,6,8,9,10}
B C = {5,6,8,9,10}{1,3,,5,7,9}= {5,9}
AC = {1,2,4,5,8} {1,3,5,7,9} ={1,5}
C B = {1,3,5,7,9} {5,6,8,9,10} ={1,3,5,6,7,8,9,10}
Distributiva:
ABC = ABAC;
ABC = {1,2,4,5,8}{5,9} = {1,2,4,5,8,9}
ABAC = {1,2,4,5,8,9,10}1,2,3,4,5,7,8,9 = {1,2,4,5,8,9}
ABC = ABAC;
ABC = {1,2,4,5,8}{1,3,5,6,7,8,9,10} = {1,5,8}
.ABAC= {5,8} {1,5} = {1,5,8}
Simplificación:
BBC ={5,6,8,9,10} {1,3,5,6,7,8,9,10} = {5,6,8,9,10}
BBC = {5,6,8,9,10} {5,9} = {5,6,8,9,10}
1ª Ley de Morgan:
.AC = A C ;
.AC = 1,2,3,4,5,7,8,9 = {6,10}
A C ={3,6,7,9,10} {2,4,6,8,10} = {6,10}2ª Ley de Morgan:
.AC = A C ;
.AC = {1,5} = {2,3,4,6,7,8,9,10}
A C = {3,6,7,9,10} {2,4,6,8,10}= {2,3,4,6,7,8,9,10}


2.Dado el espacio muestral, E= {1,2,3,4,5,6}
A= {2,4,6}
B={1,3,5}
C= {3,6}
AC = {2,4,6} {3,6}= {2,3,4,6}
AB = {2,4,6} {1,3,5} = {1,2,3,4,5,6}
B C = {1,3,5} {3,6} = {1,3,5,6}
A B= {2,4,6} {1,3,5} = {∅}
A C = {2,4,6} {3,6} = {6}
B C ={1,3,5} {3,6} = {3}
.A = {1,3,5}
.B = {2,4,6}
.C = {1,2,4,5}
A - B = A B = {2,4,6} 1,3,5 ={2,4,6} {2,4,6} = {2,4,6}
A - C = A C = {2,4,6} 1,2,4,5= {2,4}
B - C = B C = {1,3,5}{1,2,4,5} = {1,5}
Distributiva:
A (BC) = (AB) (AC) ;
A (BC) = {2,4,6} {3} = {2,3,4,6}
(AB) (AC) = {1,2,3,4,5,6} {2,3,4,6} = {2,3,4,6}
A(BC) = (AB) (AC) ;
A(BC) = {2,4,6} {1,3,5,6} = {6}(AB) (AC) = {∅}{6}= {6}

Simplificación:
A(AC) = {2,4,6} {2,3,4,6} = {2,4,6}
A (AC) = {2,4,6} {6}= {2,4,6}
1ª Ley de Morgan:
.AB = AB
.AB = {1,2,3,4,5,6} = ∅
AB = {1,3,5} {2,4,6 } = ∅...